RT-APNN for Solving Gray Radiative Transfer Equations

Fuente: arXiv
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Main Authors: Xie, Xizhe, Chen, Wengu, Ma, Zheng, Wang, Han
Format: Preprint
Published: 2025
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author Xie, Xizhe
Chen, Wengu
Ma, Zheng
Wang, Han
author_facet Xie, Xizhe
Chen, Wengu
Ma, Zheng
Wang, Han
contents The Gray Radiative Transfer Equations (GRTEs) are high-dimensional, multiscale problems that pose significant computational challenges for traditional numerical methods. Current deep learning approaches, including Physics-Informed Neural Networks (PINNs) and Asymptotically Preserving Neural Networks (APNNs), are largely restricted to low-dimensional or linear GRTEs. To address these challenges, we propose the Radiative Transfer Asymptotically Preserving Neural Network (RT-APNN), an innovative framework extending APNNs. RT-APNN integrates multiple neural networks into a cohesive architecture, reducing training time while ensuring high solution accuracy. Advanced techniques such as pre-training and Markov Chain Monte Carlo (MCMC) adaptive sampling are employed to tackle the complexities of long-term simulations and intricate boundary conditions. RT-APNN is the first deep learning method to successfully simulate the Marshak wave problem. Numerical experiments demonstrate its superiority over existing methods, including APNNs and MD-APNNs, in both accuracy and computational efficiency. Furthermore, RT-APNN excels at solving high-dimensional, nonlinear problems, underscoring its potential for diverse applications in science and engineering.
format Preprint
id arxiv_https___arxiv_org_abs_2505_14144
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle RT-APNN for Solving Gray Radiative Transfer Equations
Xie, Xizhe
Chen, Wengu
Ma, Zheng
Wang, Han
Computational Physics
The Gray Radiative Transfer Equations (GRTEs) are high-dimensional, multiscale problems that pose significant computational challenges for traditional numerical methods. Current deep learning approaches, including Physics-Informed Neural Networks (PINNs) and Asymptotically Preserving Neural Networks (APNNs), are largely restricted to low-dimensional or linear GRTEs. To address these challenges, we propose the Radiative Transfer Asymptotically Preserving Neural Network (RT-APNN), an innovative framework extending APNNs. RT-APNN integrates multiple neural networks into a cohesive architecture, reducing training time while ensuring high solution accuracy. Advanced techniques such as pre-training and Markov Chain Monte Carlo (MCMC) adaptive sampling are employed to tackle the complexities of long-term simulations and intricate boundary conditions. RT-APNN is the first deep learning method to successfully simulate the Marshak wave problem. Numerical experiments demonstrate its superiority over existing methods, including APNNs and MD-APNNs, in both accuracy and computational efficiency. Furthermore, RT-APNN excels at solving high-dimensional, nonlinear problems, underscoring its potential for diverse applications in science and engineering.
title RT-APNN for Solving Gray Radiative Transfer Equations
topic Computational Physics
url https://arxiv.org/abs/2505.14144